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At least 199 records · Page 11

Prediction of dislocation generation during Bridgman growth of GaAs crystals

Dislocation densities are generated in GaAs single crystals due to the excessive thermal stresses induced by temperature variations during growth. A viscoplastic material model for GaAs, which takes into account the movement and multiplication of dislocations in the plastic deformation, is developed according to Haasen's theory. The dislocation density is expressed as an internal state variable in this dynamic viscoplastic model. The deformation process is a nonlinear function of stress, strain rate, dislocation density and temperature. The dislocation density in the GaAs crystal during vertical Bridgman growth is calculated using a nonlinear finite element model. The dislocation multiplication in GaAs crystals for several temperature fields obtained from thermal modeling of both the GTE GaAs experimental data and artificially designed data are investigated.

Tsai, C. T.↗

Critical experiments of the self-consistent model for polycrystalline Hastelloy-X

A viscoplastic constitutive model is presented for the estimation of the overall mechanical response of Hastelloy-X polycrystalline metals from a knowledge of single crystal behavior. The behavior of polycrystal is derived from that of single crystals using a self-consistent formulation. The single crystal behavior which has been used was developed by summing postulated slip on crystallographic slip systems. The plasticity and creep are treated coupledly using unified viscoplastic model which includes the interaction effects between rapid and slow deformation at elevated temperature. The validity of the model is directly tested by experiments on Hastelloy-X in both single crystal and polycrystalline versions.

Shi, Shixiang↗

Inelastic deformation of metal matrix composites

A theoretical model capable of predicting the thermomechanical response of continuously reinforced metal matrix composite laminates subjected to multiaxial loading was developed. A micromechanical model is used in conjunction with nonlinear lamination theory to determine inelastic laminae response. Matrix viscoplasticity, residual stresses, and damage to the fiber/matrix interfacial zone are explicitly included in the model. The representative cell of the micromechanical model is considered to be in a state of generalized plane strain, enabling a quasi two-dimensional analysis to be performed. Constant strain finite elements are formulated with elastic-viscoplastic constitutive equations. Interfacial debonding is incorporated into the model through interface elements based on the interfacial debonding theory originally presented by Needleman, and modified by Tvergaard. Nonlinear interfacial constitutive equations relate interfacial tractions to displacement discontinuities at the interface. Theoretical predictions are compared with the results of an experimental program conducted on silicon carbide/titanium (SiC/Ti) unidirectional, (O4), and angle-ply, (+34)(sub s), tubular specimens. Multiaxial loading included increments of axial tension, compression, torque, and internal pressure. Loadings were chosen in an effort to distinguish inelastic deformation due to damage from matrix plasticity and separate time-dependent effects from time-independent effects. Results show that fiber/matrix debonding is nonuniform throughout the composite and is a major factor in the effective response. Also, significant creep behavior occurs at relatively low applied stress levels at room temperature.

Lissenden, C. J.↗

Time-dependent deformation of titanium metal matrix composites

A three-dimensional finite element program called VISCOPAC was developed and used to conduct a micromechanics analysis of titanium metal matrix composites. The VISCOPAC program uses a modified Eisenberg-Yen thermo-viscoplastic constitutive model to predict matrix behavior under thermomechanical fatigue loading. The analysis incorporated temperature-dependent elastic properties in the fiber and temperature-dependent viscoplastic properties in the matrix. The material model was described and the necessary material constants were determined experimentally. Fiber-matrix interfacial behavior was analyzed using a discrete fiber-matrix model. The thermal residual stresses due to the fabrication cycle were predicted with a failed interface, The failed interface resulted in lower thermal residual stresses in the matrix and fiber. Stresses due to a uniform transverse load were calculated at two temperatures, room temperature and an elevated temperature of 650 C. At both temperatures, a large stress concentration was calculated when the interface had failed. The results indicate the importance of accuracy accounting for fiber-matrix interface failure and the need for a micromechanics-based analytical technique to understand and predict the behavior of titanium metal matrix composites.

Bigelow, C. A.↗

Constitutive Theory Developed for Monolithic Ceramic Materials

With the increasing use of advanced ceramic materials in high-temperature structural applications such as advanced heat engine components, the need arises to accurately predict thermomechanical behavior that is inherently time-dependent and that is hereditary in the sense that the current behavior depends not only on current conditions but also on the material's thermomechanical history. Most current analytical life prediction methods for both subcritical crack growth and creep models use elastic stress fields to predict the time-dependent reliability response of components subjected to elevated service temperatures. Inelastic response at high temperatures has been well documented in the materials science literature for these material systems, but this issue has been ignored by the engineering design community. From a design engineer's perspective, it is imperative to emphasize that accurate predictions of time-dependent reliability demand accurate stress field information. Ceramic materials exhibit different time-dependent behavior in tension and compression. Thus, inelastic deformation models for ceramics must be constructed in a fashion that admits both sensitivity to hydrostatic stress and differing behavior in tension and compression. A number of constitutive theories for materials that exhibit sensitivity to the hydrostatic component of stress have been proposed that characterize deformation using time-independent classical plasticity as a foundation. However, none of these theories allow different behavior in tension and compression. In addition, these theories are somewhat lacking in that they are unable to capture the creep, relaxation, and rate-sensitive phenomena exhibited by ceramic materials at high temperatures. The objective of this effort at the NASA Lewis Research Center has been to formulate a macroscopic continuum theory that captures these time-dependent phenomena. Specifically, the effort has focused on inelastic deformation behavior associated with these service conditions by developing a multiaxial viscoplastic constitutive model that accounts for time-dependent hereditary material deformation (such as creep and stress relaxation) in monolithic structural ceramics. Using continuum principles of engineering mechanics, we derived the complete viscoplastic theory from a scalar dissipative potential function.

Janosik, Lesley A.↗

Fatigue Behavior of a Third Generation PM Disk Superalloy

The fatigue behavior of a 3rd generation PM disk alloy, LSHR, was studied at 1300 F. Tensile, creep, and fatigue tests were run on smooth and notched (Kt = 2) bars under a variety of conditions. Analysis of smooth bar fatigue data, run under strain and load control with R ratios of 0 and -1, showed that a stress based Smith-Watson-Topper approach could collapse the data set. While the tensile and creep data showed substantial notch strengthening at 1300 F, the fatigue data showed a life deficit for the notch specimens. A viscoplastic finite element model, which accounted for stress relaxation at the notch tip, provided the best correlation between the notched and smooth bar behavior, although the fatigue data was not fully rationalized based on this simplified viscoplastic model of the stresses at the notch tip.Inclusion of a 90 sec dwell at peak load was found to dramatically decrease notch fatigue life. This result was shown to be consistent with a simple linear creep-fatigue damage rule, where creep damage dominated at low stresses and fatigue damage was more prevalent at higher stresses.

Gayda, John↗

GVIPS Models and Software

Two reports discuss, respectively, (1) the generalized viscoplasticity with potential structure (GVIPS) class of mathematical models and (2) the Constitutive Material Parameter Estimator (COMPARE) computer program. GVIPS models are constructed within a thermodynamics- and potential-based theoretical framework, wherein one uses internal state variables and derives constitutive equations for both the reversible (elastic) and the irreversible (viscoplastic) behaviors of materials. Because of the underlying potential structure, GVIPS models not only capture a variety of material behaviors but also are very computationally efficient. COMPARE comprises (1) an analysis core and (2) a C++-language subprogram that implements a Windows-based graphical user interface (GUI) for controlling the core. The GUI relieves the user of the sometimes tedious task of preparing data for the analysis core, freeing the user to concentrate on the task of fitting experimental data and ultimately obtaining a set of material parameters. The analysis core consists of three modules: one for GVIPS material models, an analysis module containing a specialized finite-element solution algorithm, and an optimization module. COMPARE solves the problem of finding GVIPS material parameters in the manner of a design-optimization problem in which the parameters are the design variables.

Arnold, Steven M.↗

Experimental Identification and Simulation of Time and/or Rate Dependent Reversible and Irreversible Deformation Regions for both a Titanium and Nickel Alloy

In this paper time and/or rate dependent deformation regions are experimentally mapped out as a function of temperature. It is clearly demonstrated that the concept of a threshold stress (a stress that delineate reversible and irreversible behavior) is valid and necessary at elevated temperatures and corresponds to the classical yield stress at lower temperatures. Also the infinitely slow modulus, (Es) i.e. the elastic modulus of the material if it was loaded at an infinitely slow strain rate, and the "dynamic modulus", modulus, Ed, which represents the modulus of the material if it is loaded at an infinitely fast rate are used to delineate rate dependent from rate independent regions. As demonstrated at elevated temperatures there is a significant difference between the two modulus values, thus indicating both significant time-dependence and rate dependence. In the case of the nickel-based super alloy, ME3, this behavior is also shown to be grain size specific. Consequently, at higher temperatures viscoelastic behavior exist below k (i.e., the threshold stress) and at stresses above k the behavior is viscoplastic. Finally a multi-mechanism, stress partitioned viscoelastic model, capable of being consistently coupled to a viscoplastic model is characterized over the full temperature range investigated for Ti-6-4 and ME3.

Arnold, Steven M.↗

Development, Characterization, and Validation of Elevated-Temperature Constitutive Models: Deformation and Damage

This report provides a brief review of experimentally observed hereditary and nonhereditary material behavior along with background information on standard as well as advanced internal state variable constitutive modeling at elevated temperature. A description of exploratory, characterization, and validation testing is presented along with a detailed outline of what constitutes “sufficient” data content (i.e., quality and quantity) for developing or enhancing, characterizing, and validating a particular sophisticated nonlinear time- and history-dependent (hereditary) class of constitutive models known as GVIPS (generalized viscoplasticity with potential structure). The tests described are necessary to reveal a material’s behavior in the reversible (or viscoelastic) and irreversible (or viscoplastic) regimes, for the identification of both deformation and damage model parameters. Results presented are primarily for metallic materials. In all cases, both uniaxial and multiaxial tests are described, and the linkage between the specific tests and the parameters within the model that can be characterized from the results of these tests are also discussed. Discussion is also provided relative to the role information management must play relative to material data collection, analysis, maintenance, and dissemination. The need for such an information system is particularly important as both analyst and designer move toward utilizations of sophisticated, nonlinear time- and history dependent (hereditary) constitutive models. Lastly, the concept of state space and its utility in understanding and establishing constitutive models is addressed throughout. The intent behind this document is to help both the modeler and experimentalist understand each other’s specific points of view and provide guidance for both model development and characterization. Emphasis has been placed on providing the mechanician with information regarding how tests are performed and what issues to be aware of when interpreting results. It is hoped that experimentalists will take away a new perspective on the types of information that modelers and analysts are looking for from them.

Constitutive Modeling↗

An extended three-field principle to scale-bridge the granular micromechanics of polymer-bonded particulate materials

Observed phenomena of damage, viscoelasticity, and viscoplasticity in polymer-bonded particulate materials (PBPM), like polymer-bonded explosive (PBX), are accommodated in a scale-bridging constitutive model based on granular micromechanics. An extended three-field variational principle with min - max optimization problem is introduced to homogenize the bonded aggregates’ grain-scale contact mechanics. Similarly to prior applications of a three-field principle, volume constraints are invoked to embed microscale-to-macroscale correspondences for kinematic and static volumetric measures, like mean strain and its energy-conjugate stress invariant. Unlike prior applications, our three-field principle realizes a strain-driven model for effective constitutive behavior due to bonded intergranular contact. In conclusion, the resultant micro-sphere integration-based homogenization is demonstrated in comparison to existing publicly-available measurements to capture the extreme tension/compression constitutive asymmetry exhibited by PBPMs (specifically PBX-9501) during material softening.

42 ENGINEERING↗

Comparison of three state-of-the-art crystal plasticity based deformation twinning models for magnesium alloys

In magnesium alloys, deformation twinning and its interactions with dislocation slip are responsible for a sigmoidal shape stress–strain behavior and an asymmetrical tension–compression yield strength in magnesium alloys. The sensitivity of twinning to the underlying microstructure renders the crystal plasticity method the most commonly adopted modeling approach for magnesium-twinning. This paper compares three state-of-the-art crystal plasticity-based twinning models from the literature, namely the elastic-viscoplastic self-consistent twinning-detwinning (EVPSC-TDT) model, crystal plasticity finite element model based on enhanced predominate twin reorientation approach (CPFE-ePTR), and the crystal plasticity finite element model based on “discrete twinning” approach (CPFE-DT). A polycrystalline microstructure is simulated with all three methods to compare the resulting stress–strain curves and lattice strains to those from the experimentally measured data. All three methods showed the capability of capturing the experimental results with different levels of accuracy. Additionally, the EVPSC-TDT method avoids solving the finite element matrices and showed the highest computational efficiency. The CPFE-ePTR model shows a higher accuracy in capturing the lattice strain. The CPFE-DT relies on high-resolution finite element mesh and is much slower than the other two methods, but it captured the local deformation concentration and stress reversal phenomena near the twin band, which was not possible with the other two methods. Based on the comparison, guidance for the selection of the appropriate model based on the specific modeling target is provided in this paper.

36 MATERIALS SCIENCE↗

Bayesian calibration and uncertainty quantification of a rate-dependent cohesive zone model for polymer interfaces

In this work we present a rate-dependent cohesive zone model for the fracture of polymeric interfaces and performs a Bayesian calibration, an uncertainty quantification, and a sensitivity analysis for the model. The proposed cohesive zone model accounts for both reversible elastic and irreversible rate-dependent separation sliding deformation at the interface. The viscous dissipation due to the irreversible opening at the interface is modeled using elastic-viscoplastic kinematics that incorporates the effects of strain rate. Inverse calibration of parameters for such complex models through trial and error is challenging due to the large number of parameters of the model. Moreover, the calibrated parameter values are often non-unique and uncertain when the available experimental data is limited. To tackle this challenge, we employ a Bayesian calibration approach to identify parameters from experimental data, the resulting parameters significantly enhance the accuracy of the model. To quantify the uncertainty associated with the inverse parameter estimation, a modular Bayesian approach is employed to calibrate the unknown model parameters, accounting for the parameter uncertainty of the cohesive zone model. The advantages of the Bayesian calibration over a deterministic parameter fit are demonstrated. Further, to quantify the model uncertainties, such as incorrect assumptions or missing physics, a discrepancy function is introduced, which significantly improves the model’s prediction. Finally, the total uncertainty of the model is quantified in a predictive setting. A sensitivity analysis is performed to assess how changes in the input variables of the model affect the peak load, facilitating the identification of a concise set of highly influential parameters. The present approach can be used for calibration and uncertainty quantification for other complex computational mechanics models. It should also facilitate the designing of interface materials under uncertainty.

42 ENGINEERING↗

Assessment of thermal and radiation induced creep in the dual cooled lead lithium blanket

The creep in recently designed blanket for the fusion nuclear science facility is described by decomposing it into thermal, irradiation and cavity swelling creep. Initial estimates of thermal creep using elastic high temperature rules showed that the recent heat transfer improvements at the first wall (FW) is feasible, and the FW can withstand heat flux of 0.35 MW/m 2 at 3000 hrs without rupture. A viscoplastic model that is based on Norton's power law and relies on Multiphysics coupling of solid mechanics and heat transfer modules is used to capture the inelastic deformation in the blanket. Results showed that the design peak heat flux of 0.25 MW/m 2 produced maximum thermal creep strain of 0.45 % and the relaxation of the thermal stress at the FW. Irradiation creep is prescribed to be proportional to the displacement damage dose and applied stress. The displacements from irradiation creep radially decrease from the FW to the back wall, but the maximum deformation is found at the back wall that is connected to the Helium manifold due to the high stresses at the region. In conclusion, cavity swelling creep is dominant at steady state and combined with radiation creep to produce displacement of about 8 mm at the FW.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Effect of neighboring grain orientation on strain localization in slip bands in HCP materials

Particularly in plastically anisotropic crystals, such as hexagonal close packed (HCP) materials, plastic deformation is realized by slip acting in the small volumes within individual crystals. Here we extend a full field fast Fourier transform (FFT)-based elasto-viscoplastic formulation to simulate the development of a single slip band on either prismatic or basal planes spanning a crystal. Calculations of the strain and stress fields induced locally within the band and parent crystal, and ahead of the band/grain boundary junction in the neighboring crystal are analyzed as the slip band intensifies under increasing applied strain. We report a substantial influence of the crystallographic orientation of the nearest neighboring grain on the rate of slip band localization. Performing the analysis on two materials, CP-Ti and Mg, indicates that the strength of the material affects the rate of localization, with stronger materials tending to localize more easily. A slip band tip stress-based criterion is proposed for identifying the nearest neighbor orientations in which slip band transmission is possible and the likely slip system for which it occurs. This indicator is validated against experimental studies on commercially pure Ti, an Mg–Y alloy, and Ti–6Al–4V. Finally, we show that for low GB misorientations, the slip band is likely to transmit into another slip band of the same type in the neighbor grain, while for high GB misorientations, it is likely to transmit into one of a different type or to not transmit at all.

36 MATERIALS SCIENCE↗

Role of grain boundary crystallography on void growth in FCC metals

The growth of an isolated spherical void at and near a grain boundary or a triple junction is studied by means of full-field crystal plasticity simulations with explicit representation of the void. To examine the fundamental aspects of void/grain boundary interactions in these cases, a three-dimensional large-strain elasto-viscoplastic fast-Fourier transform (LS-EVP-FFT) model with axisymmetric tensile periodic boundary conditions was developed. We employ this model to reveal the role of crystallography (grain orientations, grain boundary misorientation and inclination angle with respect to the largest component of the applied stress) and type of loading on void growth. It was found that grain orientation was the primary crystallographic feature governing void growth in strain-rate controlled simulations. For strains small enough to not significantly alter the local geometry, the overall growth of the void in bicrystal boundaries was not strongly affected by grain boundary inclination angle. The relative amount of void growth experienced within each grain in a bicrystal or tri-crystal was strongly dependent on the grain boundary inclination angle. We found a subset of orientations that exhibit faster void growth in bicrystal boundaries than inside the constituent single crystals. Last, we show that when placed primarily in one grain but near the grain boundary, void growth was similar to void growth when placed at the grain boundary. Furthermore, the growing void remained in the original grain and did not grow into the other grain, regardless of crystallographic character.

36 MATERIALS SCIENCE↗

Concentration dependent properties and plastic deformation facilitate instability of the solid-electrolyte interphase in Li-ion batteries

Lithium-ion batteries (LIBs) often suffer from capacity fading and poor cyclic performance due to mechanical degradation of the solid-electrolyte interphase (SEI). Here we perform numerical simulations and theoretical analysis to elucidate the role of plasticity in wrinkling and ratcheting behaviors of an SEI/electrode system. A coupled diffusion and finite deformation framework is formulated and numerically implemented as a user-element subroutine (UEL) to describe transient lithium diffusion and accompanying elastic–viscoplastic deformation of the electrode. It is found that concentration dependent properties and plastic deformation facilitate wrinkling in such a system. A wrinkled morphology may further lead to ratcheting and related failure under cycling. A phase diagram of four types of cyclic behaviorsis identified in terms of the charging rate and time. Our analysis suggests several potential strategies to avoid wrinkling and ratcheting instabilities, such as charging/discharging the electrode at a sufficiently slow rate, and/or introducing a thick artificial SEI with a pre-tension.

25 ENERGY STORAGE↗

Yield strength of CeO 2 measured from static compression in a radial diamond anvil cell

Cerium oxide (ceria, CeO 2 ) is frequently used as a standard in applications such as synchrotron and x-ray free electron lasers for calibrating x-ray wavelengths and offers the potential for understanding the high pressure properties and deformation mechanisms in a wide range of similar face centered cubic (fcc) materials. In this study, the pressure dependence of the strength of ceria was investigated up to 38 GPa using angle dispersive x-ray diffraction in a radial geometry in a diamond anvil cell. In this experiment, the difference in the stress along the axis of compression and perpendicular to the direction of compression can be determined, giving a quantity known as the differential stress. It was found that the differential stress (t), a measure of the lower bound for yield strength, initially increases rapidly from 0.35 ± 0.06 GPa to 2.2 ± 0.4 GPa at pressures of 1.8 and 3.8 GPa, respectively. Above 4 GPa, t increases more slowly to 13.8 ± 2.6 GPa at a pressure of 38 GPa. The changes in the preferred orientation (texture) of CeO 2 with pressure were also measured, allowing for the determination of active deformation mechanisms using an elasto-viscoplastic self-consistent model (EVPSC). It was found that as pressure increased, the [001] direction had a slight preferred orientation along the axis of compression. Our EVPSC model of experimental fiber (cylindrically symmetric) textures and lattice strains were most consistent with dominant slip activity along ${111}$ $\langle$$1\bar10$$\rangle$.

36 MATERIALS SCIENCE↗

Effect of surface defects on damage and failure of dynamically driven cylindrical shells

Here, in this work, expanding cylinder experiments are performed using a gas gun on the aluminum 6061 alloy to understand the dynamic deformation and failure behavior of this material in the presence of surface defects in the form of scratches. The experiments are then modeled with the modified Tepla (for tensile plasticity) model, which is equipped with the damage yield function of Gurson [“Continuum theory of ductile rupture by void nucleation and growth: Part I—Yield criteria and flow rules for porous ductile media,” (1977)] and Tvergaard and Needleman [Acta Metall. 32(1), 157–169 (1984)], over-stress viscosity [F. Addessio and J. Johnson, J. Appl. Phys. 74(3), 1640–1648 (1993)], and the underlying viscoplastic model of Preston et al. [J. Appl. Phys. 93(1), 211–220 (2003)] (Preston–Tonks–Wallace model) for the dense material. The Tepla model parameters were calibrated using the Bayesian approach against experimentally measured free-surface velocity data obtained from plate impact experiments on the aluminum 6061 alloy. The evolution of radial expansion and shapes of the deformed cylinder from the simulations on a pristine cylinder wall and a cylinder wall with a longitudinal surface defect shows excellent agreement with the corresponding experimental results. Finally, the role of surface defect size and cylinder wall geometry on the dynamic strength of the cylinder wall was also investigated through a series of simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗